cost of producing is 50 cents each and they sell for 1.25 each. demand for programs at each game is normally distributed with a mean of 2500 and standard deviation if 200. how many shouild be prodcued
To determine the number of games that should be produced, we need to consider the cost of production, the selling price, and the demand distribution.
First, let's calculate the profit per game:
Profit = Selling Price - Cost of Production
Profit = $1.25 - $0.50
Profit = $0.75
Next, let's analyze the demand distribution. Since the demand follows a normal distribution with a mean (μ) of 2500 and a standard deviation (σ) of 200, we can use this information to calculate the probability of demand falling within certain ranges.
Now, we need to consider the profit associated with different levels of demand. Since each game has a profit of $0.75, we can calculate the expected profit (Expected Profit) by multiplying the profit per game by the probability of a certain level of demand and summing them up.
To find the optimal production quantity, we should produce enough games to maximize the expected profit. This occurs when the expected profit is maximized, which is usually when the demand is at the mean (μ).
Therefore, to maximize our profit, we should produce the number of games equal to the mean of demand (μ), which in this case is 2500.
So, the optimal quantity to produce would be 2500 games.